Triple integral over a cylindre or a sphere of the exp of the distance to a point
$begingroup$
I'm trying to solve the following integral :
$$iiint_E expleft(-a lVertvec{OC}rVertright),mathrm{d}V = iiint_E expleft(-a sqrt{(x-x_c)^2+(y-y_c)^2+(z-z_c)^2}right),mathrm{d}V$$
With $E$ being a cylinder (if a solution for a sphere exists as well, I'm interested) and $C (x_c, y_c, z_c)$ a point outside of the cylinder.
I found a few answers on mathexchange regarding this sort of integral for a sphere when $C$ is the center of the sphere (ex), but I could not find anything for a C outside of the sphere.
Wolfram|alpha did not find any solutions.
The objective is to be able to calculate auto attenuation effect in a cylinder source for direct line attenuation.
Any help would be appreciated. Thanks!
integration multiple-integral
edited Dec 5 '18 at 16:33
user10354138
7,3772925
asked Dec 5 '18 at 14:31
N. MaryN. Mary
1
$endgroup$
add a comment |
$begingroup$
I'm trying to solve the following integral :
$$iiint_E expleft(-a lVertvec{OC}rVertright),mathrm{d}V = iiint_E expleft(-a sqrt{(x-x_c)^2+(y-y_c)^2+(z-z_c)^2}right),mathrm{d}V$$
With $E$ being a cylinder (if a solution for a sphere exists as well, I'm interested) and $C (x_c, y_c, z_c)$ a point outside of the cylinder.
I found a few answers on mathexchange regarding this sort of integral for a sphere when $C$ is the center of the sphere (ex), but I could not find anything for a C outside of the sphere.
Wolfram|alpha did not find any solutions.
The objective is to be able to calculate auto attenuation effect in a cylinder source for direct line attenuation.
Any help would be appreciated. Thanks!
integration multiple-integral
edited Dec 5 '18 at 16:33
user10354138
7,3772925
asked Dec 5 '18 at 14:31
N. MaryN. Mary
1
$endgroup$
add a comment |
$begingroup$
I'm trying to solve the following integral :
$$iiint_E expleft(-a lVertvec{OC}rVertright),mathrm{d}V = iiint_E expleft(-a sqrt{(x-x_c)^2+(y-y_c)^2+(z-z_c)^2}right),mathrm{d}V$$
With $E$ being a cylinder (if a solution for a sphere exists as well, I'm interested) and $C (x_c, y_c, z_c)$ a point outside of the cylinder.
I found a few answers on mathexchange regarding this sort of integral for a sphere when $C$ is the center of the sphere (ex), but I could not find anything for a C outside of the sphere.
Wolfram|alpha did not find any solutions.
The objective is to be able to calculate auto attenuation effect in a cylinder source for direct line attenuation.
Any help would be appreciated. Thanks!
integration multiple-integral
edited Dec 5 '18 at 16:33
user10354138
7,3772925
asked Dec 5 '18 at 14:31
N. MaryN. Mary
1
$endgroup$
I'm trying to solve the following integral :
$$iiint_E expleft(-a lVertvec{OC}rVertright),mathrm{d}V = iiint_E expleft(-a sqrt{(x-x_c)^2+(y-y_c)^2+(z-z_c)^2}right),mathrm{d}V$$
With $E$ being a cylinder (if a solution for a sphere exists as well, I'm interested) and $C (x_c, y_c, z_c)$ a point outside of the cylinder.
I found a few answers on mathexchange regarding this sort of integral for a sphere when $C$ is the center of the sphere (ex), but I could not find anything for a C outside of the sphere.
Wolfram|alpha did not find any solutions.
The objective is to be able to calculate auto attenuation effect in a cylinder source for direct line attenuation.
Any help would be appreciated. Thanks!
integration multiple-integral
integration multiple-integral
edited Dec 5 '18 at 16:33
user10354138
7,3772925
asked Dec 5 '18 at 14:31
N. MaryN. Mary
1
edited Dec 5 '18 at 16:33
user10354138
7,3772925
asked Dec 5 '18 at 14:31
N. MaryN. Mary
1
edited Dec 5 '18 at 16:33
user10354138
7,3772925
edited Dec 5 '18 at 16:33
user10354138
7,3772925
edited Dec 5 '18 at 16:33
user10354138
7,3772925
7,3772925
asked Dec 5 '18 at 14:31
N. MaryN. Mary
1
asked Dec 5 '18 at 14:31
N. MaryN. Mary
1
asked Dec 5 '18 at 14:31
N. MaryN. Mary
1
1
add a comment |
add a comment |
1 Answer
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I might be totally incorrect, as I haven't seen calculus in a long time, but I would think it would be a good opportunity to change to cylindrical coordinates and use the jacobian.
If this isn't toally nonsense, I'd be happy to try and write it for you assuming dV=dxdydz and xc, yc, zc, and a are constants.
answered Dec 5 '18 at 16:50
nessness
375
$endgroup$
$begingroup$
Yes, a and the coordinate of C are constants. Feel free to give it a try, thanks
$endgroup$
– N. Mary
Dec 6 '18 at 10:46
add a comment |
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1 Answer
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$begingroup$
I might be totally incorrect, as I haven't seen calculus in a long time, but I would think it would be a good opportunity to change to cylindrical coordinates and use the jacobian.
If this isn't toally nonsense, I'd be happy to try and write it for you assuming dV=dxdydz and xc, yc, zc, and a are constants.
answered Dec 5 '18 at 16:50
nessness
375
$endgroup$
$begingroup$
Yes, a and the coordinate of C are constants. Feel free to give it a try, thanks
$endgroup$
– N. Mary
Dec 6 '18 at 10:46
add a comment |
$begingroup$
I might be totally incorrect, as I haven't seen calculus in a long time, but I would think it would be a good opportunity to change to cylindrical coordinates and use the jacobian.
If this isn't toally nonsense, I'd be happy to try and write it for you assuming dV=dxdydz and xc, yc, zc, and a are constants.
answered Dec 5 '18 at 16:50
nessness
375
$endgroup$
$begingroup$
Yes, a and the coordinate of C are constants. Feel free to give it a try, thanks
$endgroup$
– N. Mary
Dec 6 '18 at 10:46
add a comment |
$begingroup$
I might be totally incorrect, as I haven't seen calculus in a long time, but I would think it would be a good opportunity to change to cylindrical coordinates and use the jacobian.
If this isn't toally nonsense, I'd be happy to try and write it for you assuming dV=dxdydz and xc, yc, zc, and a are constants.
answered Dec 5 '18 at 16:50
nessness
375
$endgroup$
I might be totally incorrect, as I haven't seen calculus in a long time, but I would think it would be a good opportunity to change to cylindrical coordinates and use the jacobian.
If this isn't toally nonsense, I'd be happy to try and write it for you assuming dV=dxdydz and xc, yc, zc, and a are constants.
answered Dec 5 '18 at 16:50
nessness
375
edited Dec 5 '18 at 16:56
answered Dec 5 '18 at 16:50
nessness
375
answered Dec 5 '18 at 16:50
nessness
375
answered Dec 5 '18 at 16:50
nessness
375
375
$begingroup$
Yes, a and the coordinate of C are constants. Feel free to give it a try, thanks
$endgroup$
– N. Mary
Dec 6 '18 at 10:46
add a comment |
$begingroup$
Yes, a and the coordinate of C are constants. Feel free to give it a try, thanks
$endgroup$
– N. Mary
Dec 6 '18 at 10:46
$begingroup$
Yes, a and the coordinate of C are constants. Feel free to give it a try, thanks
$endgroup$
– N. Mary
Dec 6 '18 at 10:46
$begingroup$
Yes, a and the coordinate of C are constants. Feel free to give it a try, thanks
$endgroup$
– N. Mary
Dec 6 '18 at 10:46
add a comment |
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